Model-Based Uncertainty in Value Functions (2302.12526v2)

Abstract: We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty BeLLMan equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty BeLLMan equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency.

• The paper introduces a refined uncertainty Bellman equation that converges to the true posterior variance over values, eliminating over-conservatism in exploration.
• It leverages Bayesian methods to isolate epistemic uncertainty from aleatoric noise, achieving more accurate uncertainty quantification.
• Sharper uncertainty estimates enhance sample efficiency and promote balanced exploration-exploitation strategies in both tabular and deep RL settings.

Model-Based Uncertainty in Value Functions

The paper explores the challenge of accurately quantifying the uncertainty associated with expected cumulative rewards in Model-Based Reinforcement Learning (MBRL) by focusing on the variance over values induced by a distribution over Markov Decision Processes (MDPs). Existing approaches provide upper bounds on the posterior variance of value functions using the uncertainty BeLLMan equation; however, these methods often lead to excessive conservatism and inefficient exploration due to over-approximation. The authors propose a refined uncertainty BeLLMan equation that converges on the true posterior variance over values, clearly delineating the discrepancy with previous methods.

Technical Contributions and Results

The work contributes a novel uncertainty BeLLMan equation that guarantees convergence to the actual posterior variance over values without the necessity for over-estimation. This improved characterization of uncertainty leverages Bayesian methods to quantify not only epistemic uncertainty within model uncertainty but distinguishes it from aleatoric noise inherent to MDPs. The posterior variance result applies under assumptions such as acyclic MDPs and independence of transition functions over different state-action pairs. The method extends beyond the tabular representation through compatibility with the existing Deep RL architectures.

The authors' experimental analysis indicates that sharper uncertainty estimates result in improved sample efficiency for deep exploration in complex environments, both tabular and those requiring continuous control. Such results suggest that accurate quantification of uncertainty can lead to more balanced exploration-exploitation strategies that are crucial in data-efficient MBRL.

Implications and Future Directions

Separating epistemic from aleatoric uncertainty in MBRL has significant implications for the design of exploration strategies. This work suggests that more effective exploration can be accomplished by focusing on regions of high epistemic uncertainty where learning is most valuable, thus guiding agents towards informative states.

Future research may involve extending this uncertainty estimation approach to various classes of policies and MDPs, including those with unknown reward structures. Additionally, exploration into leveraging these insights to design adaptive policies that dynamically adjust their explorative behavior based on uncertainty estimates could further enhance the applicability and efficiency of MBRL in real-world scenarios.

The work provides an essential step towards refining existing exploration frameworks in RL by offering a more precise tool for handling uncertainty, which could catalyze advancements in AI systems that require safe and reliable decision-making capabilities in uncertain and dynamic environments.